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Growing a Dynamic Array

Simulate how a dynamic array doubles its capacity and count the reallocations and copied elements.

Lo que aprenderás

  • See how a vector doubles its capacity
  • Count copies made during reallocation
  • Understand why appending stays fast on average

Problema

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A dynamic array such as C++ std::vector stores its elements in one block of memory. When the block is full and a new element arrives, it allocates a block twice as large, copies the existing elements over, and frees the old one.

Start with an empty array of capacity initial_capacity and push pushes elements one by one. Before each push, if size == capacity, reallocate: count one reallocation, add the current size to the copied elements, and double the capacity.

Implement dynamic_array_growth(pushes, initial_capacity).

Input

pushes: How many elements are pushed.

initial_capacity: The capacity of the empty array.

Output

Return [reallocations, copied_elements, final_capacity].

Restricciones

0 ≤ pushes ≤ 10^7

1 ≤ initial_capacity ≤ 10^6

Ejemplos

Ejemplo 1
Entrada:
pushes = 5
initial_capacity = 1

Salida esperada:
expected = [3, 7, 8]
Entrada:
long long pushes = 5;
long long initial_capacity = 1;

Salida esperada:
std::vector<long long> expected = {3, 7, 8};
Entrada:
long pushes = 5;
long initial_capacity = 1;

Salida esperada:
long[] expected = new long[] {3, 7, 8};

Explicación

Capacity grows 1 → 2 → 4 → 8 when pushing the 2nd, 3rd and 5th elements, copying 1 + 2 + 4 = 7 elements: [3, 7, 8].

Ejemplo 2
Entrada:
pushes = 4
initial_capacity = 4

Salida esperada:
expected = [0, 0, 4]
Entrada:
long long pushes = 4;
long long initial_capacity = 4;

Salida esperada:
std::vector<long long> expected = {0, 0, 4};
Entrada:
long pushes = 4;
long initial_capacity = 4;

Salida esperada:
long[] expected = new long[] {0, 0, 4};

Explicación

All four elements fit in the first block, so nothing is reallocated: [0, 0, 4].

Cómo abordarlo

Inténtalo primero por tu cuenta y luego abre las pistas una a una.

Pista 1

A reallocation happens only when the array is full.

Pista 2

Each time, all current elements are copied and the capacity doubles.

Pista 3

You can jump from one doubling to the next instead of simulating every push.

Complejidad esperada

O(log pushes) time, O(1) extra space

Referencias

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